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Many real-world applications require the joint optimization of a large numberof flexible devices over some time horizon. The flexibility of multiplebatteries, thermostatically controlled loads, or electric vehicles, e.g., canbe used to support grid operations and to reduce operation costs. Usingpiecewise constant power values, the flexibility of each device over $d$ timeperiods can be described as a polytopic subset in power space. The aggregatedflexibility is given by the Minkowski sum of these polytopes. As thecomputation of Minkowski sums is in general demanding, several approximationshave been proposed in the literature. Yet, their application potential is oftenobjective-dependent and limited by the curse of dimensionality. In this paper,we show that up to $2^d$ vertices of each polytope can be computed efficientlyand that the convex hull of their sums provides a computationally efficientinner approximation of the Minkowski sum. Via an extensive simulation study, weillustrate that our approach outperforms ten state-of-the-art innerapproximations in terms of computational complexity and accuracy for differentobjectives. Moreover, we propose an efficient disaggregation method applicableto any vertex-based approximation. The proposed methods provide an efficientmeans to aggregate and to disaggregate typical battery storages inquarter-hourly periods over an entire day with reasonable accuracy foraggregated cost and for peak power optimization.

Alleviating the Curse of Dimensionality in Minkowski Sum Approximations of Storage Flexibility